On page 116, you mention that Ueshiba received a Shinkage-ryu menkyo from Takeda. You mention that Sokaku is not known to have studied such a system.

But, on page 125, you write that Gejo Kosaburo, a shihan in Yagyu Shinkage-ryu was a friend of Sokaku Takeda.

Also you write that Otsubo of Yagyu Shinkage-ryu gave Ueshiba a compliment that "You must have studied Yagyu-ryu somewhere".

How close were Takeda and Gejo Kosaburo? Could Takeda have learned (informally) Yagyu Shinkage-ryu from Gejo? In some manner? And could that have been what Takeda gave to Ueshiba in the form of the Shinkage-ryu menkyo? If so, it would explain Otsubo's words.